Temperature distribution measuring apparatus using an optical fiber

ABSTRACT

A temperature distribution measuring apparatus and related method uses optical time domain reflectometry to determine temperature distribution along an optical fiber. A light pulse enters the fiber at one end, and backscattered light at each of various points in the optical fiber has a Raman spectrum which contains temperature information. An impulse response to the Raman spectra of backscattered light is produced using a transformation to provide a temperature distribution along the optical fiber. An impulse response on the anti-Stokes component and an impulse response of the Stokes component of the Raman spectrum are each produced, and the ratio between them indicates temperature distribution. Each impulse response is obtained by performing deconvolution on the Stokes component and the anti-Stokes component using an inverse matrix of measured incident light, the inverse matrix being obtained by an iteration method with an optimum number of iterations.

This is a division of application Ser. No. 08/528,594, filed Sep. 15,1995, now U.S. Pat. No. 5,639,162, issued Dec. 12, 1996, which is acontinuation of Ser. No. 08/177,324, filed Jan. 4, 1994, now abandoned.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to a temperature distribution measuringapparatus which projects pulsed-light into an optical fiber, measuresthe Raman spectrum of backscattered light occurring in the opticalfiber, and determines a temperature distribution along the opticalfiber.

2. Description of the Related Art

In the field of optical sensing technology, a temperature distributionmeasuring apparatus using optical time domain reflectometry (OTDR)techniques is known which allows pulsed-light to enter an optical fiberat one end, samples and measures the Raman spectrum of backscatteredlight at various points in the optical fiber, and determines from thesampling data a temperature distribution along the optical fiber.

FIG. 1 is a schematic diagram illustrating the measuring principle of aconventional temperature distribution measuring apparatus of this type.A laser pulse enters an optical fiber 100 to excite backscattered lightin the optical fiber 100. The spectrum intensity, and polarization stateof the backscattered light contain temperature information at the pointwhere the backscattered light has occurred. The backscattered light thatpropagates toward the laser-pulse incident side is sensed and processedas a time-sequence signal. A one-dimensional temperature distributionalong the optical fiber is thus measured.

The backscattered light occurring when a laser pulse enters the opticalfiber 100 includes the Rayleigh spectrum due to fluctuations in density,the Brillouin spectrum due to propagative fluctuations, and the Ramanspectrum due to rotation and vibration of molecules. The Brillouinspectrum and the Raman spectrum are inelastic scattered light and have adifferent spectrum from that of the excited light. The temperatureinformation is contained in all three types of scattered light. The mosttemperature-sensitive spectrum is the Raman spectrum, whose intensityvaries with temperature.

When the temperature is measured using the Raman spectrum, the Stokescomponent of the Raman spectrum of the backscattered light whosewavelength becomes longer than that of the incident light and theanti-Stokes component of the Raman spectrum of the backscattered lightwhose wavelength becomes shorter than that of the incident light areextracted by an optical filter, and the temperature distribution iscalculated based on the ratio between the two components ofbackscattered light. Of course, the measurement can be performed on thebasis of only one component of the Raman spectrum of the backscatteredlight. In both cases, however, at least one component of the Ramanspectrum of the backscattered light must be extracted by an opticalfilter.

In such a temperature distribution measuring apparatus, not only theaccuracy of temperature, a physical quantity to be measured but also itspositional resolution is important. The positional resolution isgenerally determined by the incident pulse width. It further depends onthe sampling frequency when the processing system of the backscatteredlight is a sampled-value system.

If the sampling period is sufficiently shorter than half the width ofthe incident light pulses, the measured backscattered light is the totalof the backscattered light for half the width of the incident lightpulses. Therefore, the measured temperature is the average temperatureover half the pulse width. Even if the sampling frequency becomes fast,the positional resolution cannot be increased more than the width of theincident pulse.

Therefore, to increase the positional resolution, narrowing the pulsewidth of the incident light is effective. To achieve this, two methodscan be considered: one is to actually narrow the width of the incidentpulsed-light itself, and the other is to consider a response of thebackscattered light to a light pulse of a finite width to be atransformation, and to obtain an impulse response by performing aninverse transformation of the measured value of the backscattered light.

Since narrowing the pulse width alone cannot make the width of a lightpulse narrower than the pulse width determined by the rising and fallingcharacteristics of a source of pulsed-light, it is difficult to make thewidth of the incident pulse narrower than that achieved by the elementsalready developed. Thus, this method is unsuitable for increasing thepositional resolution.

In contrast, a method of obtaining an impulse response is consideredeffective in increasing the positional resolution.

Therefore, the method of obtaining an impulse response will be examined.

Since the transformation used in the method of obtaining an impulseresponse is a convolution in a range of linear approximation, if theimpulse response is expressed as h(t) and the incident pulsed-light isexpressed as P(t), the backscattered light signal g(t) will be obtainedby performing convolution of the impulse response h(t) with respect tothe incident light pulse P(t). It can be expressed as: ##EQU1##

Then, the impulse response h(t) can be obtained by measuring theincident light pulse P(t), an input signal, and performing deconvolutionof the measured backscattered light signal g(t) with respect to theincident light pulse P(t).

Actually, however, even if deconvolution is performed on the measureddata, it is difficult to obtain the correct impulse response because themeasured signal contains noise components. The reason for this will bedescribed below.

By achieving the Fourier transform of Equation (1) and adding noisecomponent N(ω) to the backscattered light, the following equation willbe obtained:

    G(ω)+N(ω)=H(ω)P(ω)                 (2)

For inverse transformation, by dividing both sides of Equation (2) byP(ω), the following equation is obtained:

    H(ω)=G(ω)/P(ω)+N(ω)/P(ω)     (3)

Here, the second term on the right side of Equation (3) is a problem.While the spectrum of incident light pulse component P(ω) is finite, thespectrum of noise component N(ω) extends over a very wide range, thus,the division result diverges in the high-frequency range (where theangular velocity ωis large).

This divergence makes it impossible to obtain the impulse responsecorrectly, so that the positional resolution cannot be improved asexpected, thus reducing the total accuracy of position measurement.

SUMMARY OF THE INVENTION

Accordingly, it is an object of the present invention to provide atemperature distribution measuring apparatus which projects pulsed-lightinto an optical fiber and measures the Raman spectrum of backscatteredlight occurring in the optical fiber to obtain a temperaturedistribution along the optical fiber and particularly which can obtainan impulse response of an incident light accurately from the measuredvalue of the backscattered light and improve a positional resolution ofthe temperature distribution.

According to the present invention, there is provided an apparatus formeasuring a temperature distribution along an optical fiber, comprisinglight source means for projecting pulsed-light into the optical fiber;optical filter means for receiving Raman spectrum of backscattered lightoccurred in the optical fiber and extracting the anti-Stokes componentand Stokes component of the Raman spectrum of the backscattered light;means for obtaining an impulse response of the anti-Stokes component andan impulse response of the Stokes component by performing deconvolutionon the Stokes component and the anti-Stokes component using an inversematrix of incident pulsed-light, the inverse matrix obtained by aniteration method with an optimum number of iterations; means forobtaining a temperature distribution according to a ratio between theimpulse responses of the anti-Stokes component and the Stokes component;and means for causing the temperature distribution obtaining means toobtain the temperature distribution in a portion as long as or shorterthan a half-width of the pulsed-light where the temperature is known,determining the optimum number of iterations that an error between aknown temperature and an obtained temperature is minimum.

According to the present invention, there is provided another apparatusfor measuring a temperature distribution along an optical fiber,comprising light source means for projecting pulsed-light into theoptical fiber; means for sensing Fresnel reflected light from an end ofthe optical fiber; means for performing a deconvolution a plurality oftimes on the Fresnel reflected light, the number of times performing thedeconvolution being determined such that a result of the deconvolutionshows an impulse response waveform; optical filter means for receivingRaman spectrum of backscattered light from the optical fiber andextracting anti-Stokes component and Stokes component of the Ramanspectrum in the backscattered light; means for performing adeconvolution a plurality of times on the anti-Stokes component and theStokes component to obtain an impulse response of the anti-Stokescomponent and an impulse response of the Stokes component, the number oftimes the deconvolution is to be performed on the Stokes and anti-Stokescomponents corresponding to the number of times the deconvolution isperformed on the Fresnel reflected light; and means for obtaining atemperature distribution according to a ratio between the impulseresponses of the anti-Stokes component and the Stokes component.

Additional objects and advantages of the present invention will be setforth in the description which follows, and in part will be obvious fromthe description, or may be learned by practice of the present invention.The objects and advantages of the present invention may be realized andobtained by means of the instrumentalities and combinations particularlypointed out in the appended claims.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings, which are incorporated in and constitute apart of the specification, illustrate presently preferred embodiments ofthe present invention and, together with the general description givenabove and the detailed description of the preferred embodiments givenbelow, serve to explain the principles of the present invention inwhich:

FIG. 1 is a schematic diagram of a conventional temperature distributionmeasuring apparatus based on the OTDR technique;

FIG. 2 shows the principle of the temperature distribution measuringapparatus according to the present invention;

FIG. 3 shows the basic configuration for implementing the principle ofthe temperature distribution measuring apparatus according to thepresent invention;

FIG. 4 shows a temperature distribution waveform obtained by theconfiguration of FIG. 3;

FIGS. 5A, 5B, and 5C show the effects of deconvolution of thetemperature distribution waveform shown in FIG. 4;

FIG. 6 shows the relationship between the number of iterations forobtaining an inverse matrix of incident light used in deconvolution anderror;

FIGS. 7A, 7B, and 7C show the effects of deconvolution when thereference temperature portion is made longer than the half-width of theincident pulsed-light;

FIG. 8A, 8B, and 8C show the effects of deconvolution when the referencetemperature portion is made shorter than the half-width of the incidentpulsed-light;

FIG. 9 is a block diagram of the overall configuration of a temperaturedistribution measuring apparatus according to a first embodiment of thepresent invention;

FIG. 10 shows the principle of a temperature distribution measuringapparatus according to a second embodiment of the present invention; and

FIG. 11 is a block diagram of the overall configuration of a temperaturedistribution measuring apparatus of the second embodiment.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

A preferred embodiment of a temperature distribution measuring apparatusaccording to the present invention will now be described with referenceto the accompanying drawings.

Before going into explanation of a temperature distribution sensingapparatus according to the present invention, the principle of measuringtemperature distribution will be described.

If in an optical fiber for temperature measurement, the backscatteringcoefficient per unit length is S(z), an attenuation factor that theincident light pulse suffers while traveling in the optical fiber isR_(f) (z), an attenuation factor that the backscattered light suffers inthe optical fiber until it reaches the incident end is R_(b) (z), and agroup velocity of pulsed-light in the optical fiber is Vg, the impulseresponse (power) h(t) of the backscattered light obtained by projectingpulsed-light into the optical fiber (and is included in Equation (1)) isexpressed by the following expression:

    h(t)=R .sub.f (z)S(z)R .sub.b (z)Vg/2                      (4)

As shown in Equation (1), the backscattered light g(t) is obtained byperforming convolution on the impulse response with respect to theincident light P(t). To be more specific, what are convoluted with theincident light P(t) in the scattering process are coefficients Sa(z) ofthe anti-Stokes component and Ss(z) of the Stokes component of the Ramanspectrum of the backscattered light. After the backscattered lights ofthe anti-Stokes component and the Stokes component of the Raman spectrumare inversely transformed (subjected to deconvolution) to obtain theimpulse responses of the anti-Stokes component and the Stokes componentof the Raman spectrum of the backscattered light, the temperaturedistribution is calculated based on the ratio between these two impulseresponses in order to compensate for the attenuation effect of theoptical fiber.

To obtain the impulse response, in the actual apparatus, after thebackscattered light is converted into an electric signal with aphotodiode or the like, the resulting signal undergoes A/D conversionand the converted signal is treated as the sampled-value system digitalsignal. Thus, the convolution given by integral Equation (1) isexpressed as follows: ##EQU2##

Equation (5) can be illustrated by an n×n matrix that has only diagonalcomponents where the position of the incident pulse moves as timeelapses, as shown in FIG. 2. In equation (5), n corresponds to thenumber of positions along the optical fiber. In this case, the elementsin each row of the incident light Pij are the measured values of thepulsed-light waveform in the order of measurement.

Thus, to obtain the impulse response hj, it is necessary to multiplyboth sides of Equation (5) by the inverse matrix of the incident lightPij. Multiplication by the inverse matrix of the incident light Pijcorresponds to deconvolution. For obtaining the impulse response whilemonitoring the influence of noise, a method of converging the solution(the inverse matrix) using an iteration method (for example, Jacobimethod or Gauss-Seidel method) is suitable.

In an iteration method, if the number of iterations is "k" and the i-thsolution (the final solution of the present invention is to obtain theimpulse response) in the k-th iteration is hi.sup.(k), the i-th solutionhi.sup.(k+1) in the (k+1)th iteration is expressed as: ##EQU3## where dis a constant.

The number of iterations of an iteration method for obtaining theimpulse response hi will be explained. As shown in FIG. 3, a signalprocessing device 101, an 80° C. thermostat chamber 102, and a 1-Kmoptical fiber 103 are prepared. Specified portions of 2 m, 5 m, 10 m, 20m, and 50 m long respectively, of the optical fiber 103 are put in thethermostatic chamber 102 to keep them at 80° C. With the specifiedportions kept at this temperature, the signal processing device 101(also having the function of projecting a laser pulse) measures theanti-Stokes component and the Stokes component of the Raman spectrum ofthe backscattered light by OTDR technique. Then, computing the ratiobetween the anti-Stokes component and the Stokes component along theoptical fiber gives a waveform shown in FIG. 4.

In this case, all the computation results for the specified portionsplaced in the thermostatic chamber 102 should be the same. Actually,however, as apparent from FIG. 4, a sufficient amplitude cannot beobtained for the portions shorter than 10 m of the optical fiber 103,that is, the 5-m and 2-m-long portions, due to convolution, because thehalf-width of the light pulse used in the measurement is 200 nsec andcorresponds to 10 m of the optical fiber. The half-width of the lightpulse is the half-period of the light pulse, i.e., the reciprocal of thefrequency. The product of the half-width or half-period with the speedof light, c (3×10⁸ m/sec) produces the half-wavelength of the lightpulse. The refractive index of the optical fiber is based on thewavelength of the incident light pulse. The velocity of the incidentlight pulse is reduced from the speed of light by the refractive index,i.e., c divided by the refractive index. Thus, based on the half-widthof the light pulse, the distance the half-width light pulse travels canbe determined by multiplying the half-width by c and dividing theproduct by the refractive index. Therefore, the half-width of the lightpulse, although measured in time, corresponds to the length traveled inthe optical fiber.

To eliminate such an effect of convolution, the impulse response wasobtained by performing deconvolution of the measured data of thebackscattered light acquired through the above measurement, with respectto the incident light.

When the waveform of the measured data before deconvolution was as shownin FIG. 5A, performing deconvolution of this data using the inversematrix of the incident light obtained by an iteration method with fiveiteration times gave a waveform shown in FIG. 5B; performingdeconvolution of this data using the inverse matrix obtained by aniteration method with ten iteration times gave a waveform shown in FIG.5C.

As seen from FIGS. 5A, 5B, and 5C, deconvolution can improve not only aninsufficient amplitude of the measured data, but also the rising/fallingcharacteristic.

Although such improvements can be achieved, it is found that as thenumber of iterations of an iteration method for obtaining the inversematrix increases, the effect of noise becomes more significant.

Here, errors such as the amplitude that do not reach a specified valuedue to the effect of convolution (as shown in FIG. 4, errors appear inthat portion of which length is less than half the width of the pulse ofthe incident light) are defined as system errors, and variations due tothe influence of noise are defined as random errors. To examine therelationship between the number of iterations for obtaining the inversematrix of the incident light by an iteration method, the system error,and the random error, deconvolution was performed on the 5-m-long heatedportion, using the data on the portion immediately before the heatedportion as the random error. This deconvolution produced the results forthe total error shown in FIG. 6.

As obvious from FIG. 6, as the number of iterations is increased, randomerrors increase at a constant rate. System errors, however, firstcontinue to decrease at a constant rate until a certain number ofiterations is reached, and thereafter increase at a constant rate.

Thus, there is an optimum number of iterations that minimizes the totalerror obtained by adding the system error and the random error.Specifically, when the temperature distribution is exactly known as inthe case of the optical fiber 103 placed in the thermostatic chamber 102of FIG. 3, the difference between the measured value and the knowntemperature is computed for each iteration. By finding the smallest ofthe results, the optimum number of iterations can be obtained. Contraryto the present invention, a conventional iteration method finds out asuitable iteration number based on the degree of convergence of thesolution. In a conventional iteration method, an iteration is ended ifthe difference between a current solution and a previous solutionbecomes less than a predetermined level. However, the solution thusobtained cannot ensure that the total error is minimum. According to thepresent invention, however, it is possible to obtain the optimumsolution having the minimum error.

In such a deconvolution method, however, as the number of iterations forobtaining the inverse matrix increases, random noise increases. Thus,where there are few system errors, for example, where the temperaturedistribution is almost uniform, only random errors increase. Therefore,it is when the temperature distribution is measured where thetemperature changes significantly with respect to space, especiallywhere the temperature is locally very high and low that thisdeconvolution method is effective.

Therefore, a plant control system to which such a deconvolution methodis applied is a system where an abnormality in the system appears as alocal temperature rise. In such a system, when the temperature riseslocally, applying the optimum number of iterations enables the efficientsensing of the temperature rise.

With the present invention, to find the optimum number of iterations ofan iteration method for obtaining an inverse matrix of the incidentlight which is deconvoluted with the measured value of the backscatteredlight, at least a portion of an optical fiber shorter than half thewidth of the incident light pulse is heated or cooled to use this heatedor cooled portion as a reference temperature portion, and the number ofiterations that the total accuracy of the reference temperature portionis best improved is determined. In an actual measurement, deconvolutionis performed to obtain an impulse response using an inverse matrix ofthe incident light which is calculated by an iteration method with anoptimum number of iterations. This makes it possible to improve thepositional resolution remarkably while minimizing the effect of noise inmeasuring the temperature distribution by means of an optical fiber.

In this case, when the reference temperature portion (FIG. 7A) is longerthan half the width of the incident light pulse (FIG. 7B), the measuredvalue (FIG. 7C) has a sufficient amplitude to obtain the correcttemperature. Therefore, the effect of deconvolution is not great. Withthe present invention, however, the reference temperature portion (FIG.8A) is made shorter than half the width of the incident light pulse(FIG. 8B), so that the measured value (FIG. 8C) has an insufficientamplitude. Therefore, the effect of deconvolution is great. An amplitudeof the measured value is increased by means of deconvolution.

FIG. 9 is a schematic diagram of a temperature distribution measuringapparatus according to a first embodiment of the present invention basedon such principles.

The first embodiment comprises an optical fiber 1, a signal processingdevice 3 which projects light pulse into the optical fiber 1, senses thebackscattered light from the optical fiber 1, and measures thetemperature distribution along the optical fiber 1 on the basis of theratio of the anti-Stokes component to the Stokes component of the Ramanspectrum of the backscattered light, and a reference temperature chamber2 in which one end of the optical fiber 1 on the side of the signalprocessing device 3 is placed.

At the time of initialization and at regular intervals during the actualmeasurement, a portion of the optical fiber 1 is heated to a hightemperature by the reference temperature chamber 2 with another portionkept at room temperature. In this state, the signal processing device 3produces very narrow light pulse and projects it into the opticalfiber 1. Thereafter, it takes in the backscattered light, obtains theimpulse response on the basis of the anti-Stokes component and theStokes component of the Raman spectrum of the backscattered light by aniteration method for obtaining the inverse matrix used in deconvolution,and finds the optimum number of iterations that the total error becomesthe smallest.

For an actual measurement, the signal processing device 3 generatesincident light pulses having a very narrow pulse width and projects itinto the optical fiber 1. It then takes in the backscattered light,obtains the impulse responses of the anti-Stokes component and theStokes component of the Raman spectrum of the backscattered light by aniteration method with the optimum number of iterations, and measures thetemperature distribution at each point where the optical fiber is laid,on the basis of a ratio of these impulse responses.

The optical fiber 1 is laid so as to pass through each portion where thetemperature is to be measured. A portion of the optical fiber 1 isheated to a high temperature by the reference temperature chamber 2,while another portion of the optical fiber is kept at room temperature.When light pulse arrives at its incident end, the optical fiber 1 takesit in and returns the backscattered light to the incident end accordingto the temperature at each portion.

The reference temperature chamber 2 comprises a room temperatureenclosure 4 in which a portion of the optical fiber 1 is housed, atemperature sensor 5 which is placed in the room temperature enclosure 4and which measures the temperature in the room temperature enclosure 4and supplies the measurement result to the signal processing device 3, arectangular high-temperature enclosure 6 which is placed so as to beadjacent to the room temperature enclosure 4 and which houses anotherportion of the optical fiber 1 shorter than the half-width of the lightpulse output from the signal processing device 3, a temperature sensor 7which is placed in the high-temperature enclosure 6 and which measuresthe temperature in the high-temperature enclosure 6 and supplies themeasurement result to the signal processing device 3, a heater 8 placedin the high-temperature enclosure 6, and a heater controller 9 which,when the signal processing device 3 is issuing a high-temperatureinstruction, actuates the heater 8 on the basis of the measurementresult from the temperature sensor 7 to heat the temperature in thehigh-temperature enclosure 6 to a predetermined temperature. While inFIG. 9, the optical fiber 1 is looped in the enclosures 4 and 6 to makethem compact, it is not necessarily looped. The optical fiber 1 may bestraight in the enclosures 4 and 6.

The temperature sensor 5 measures the temperature in the roomtemperature enclosure 4 and supplies the measurement result to thesignal processing device 3. The temperature sensor 7 measures thetemperature in the high-temperature enclosure 6 and supplies themeasurement result to the signal processing device 3 and the heatercontroller 9. When the signal processing device 3 is issuing ahigh-temperature instruction, the heater controller 9 actuates theheater 8 on the basis of the measurement result from the temperaturesensor 7 to raise the temperature in the high-temperature enclosure 6 tothe predetermined high temperature, thereby bringing a portion of theoptical fiber 1 housed in the high-temperature enclosure 6 into ahigh-temperature state.

The signal processing device 3 comprises a timing controller 12, a laserdriver 13, a laser light source 14, a coupler 15, an optical filter 16,an optical selector 17, a bias controller 18, a photodiode 19, aphotocurrent amplifier circuit 20, a digital averager 21, and a CPU 22.

The pulsed-laser light from the laser light source 14, such as asemiconductor laser, is directed to enter an incident end of the opticalfiber 1 via the coupler 15. The laser light source 14 is actuated by thelaser driver 13 controlled by the timing controller 12. The timingcontroller 12 is controlled by the CPU 22.

The backscattered light emitted from the optical fiber 1 goes throughthe coupler 15 and is separated by the optical filter 16 into the Stokescomponent and the anti-Stokes component of the Raman spectrum of thebackscattered light. One of the two components is selected by theoptical selector 17 and is allowed to enter the photodiode 19. Thephotodiode 19 is controlled by the bias controller 18. The outputcurrent of the photodiode 19 is supplied to the digital averager 21 viathe photocurrent amplifier 20. The digital averager 21 averages themeasurement results of backscattered light to many incidences ofpulse-light. Since the backscattered light has a very small amplitude,the measured value is obtained based on the average value of manymeasurements. The output of the averager 21 is supplied to the CPU 22.The CPU 22 is connected to a temperature distribution output interface(not shown).

At the time of initialization and at regular intervals during the actualmeasurement, the signal processing device 3 causes the referencetemperature chamber 2 to raise a portion of the optical fiber 1 placedin the high-temperature enclosure 6 to a high temperature, while keepinganother portion of the optical fiber 1 placed in the room-temperatureenclosure 4 at room temperature. In this state, the signal processingdevice 3 produces very narrow pulsed-light and projects it into theoptical fiber 1. It then takes in the backscattered light and obtainsthe impulse responses of the anti-Stokes component and the Stokescomponent of the Raman spectrum of the backscattered light by aniteration method. It should be noted that the backscattered light ismeasured on the basis of the averaged value of many incidents ofpulsed-light. While computing the temperature distribution from theratio between these two impulse responses, it finds the optimum numberof iterations for obtaining the inverse matrix used in deconvolutionthat the total error becomes the smallest.

For an actual measurement, the signal processing device 3 generatesincident pulsed-light having a very narrow pulse light and projects itinto the optical fiber 1. It then takes in its backscattered light,obtains the impulse responses of the anti-Stokes component and theStokes component of the Raman spectrum of the backscattered light by aniteration method with the optimum number of iterations, and measures thetemperature distribution at each point where the optical fiber is laid,on the basis of the ratio between these two impulse responses.

The timing controller 12 together with the CPU 22 produces alight-emission timing signal, a synchronous addition timing signal, etc.It supplies the light-emission timing signal to the laser driver 13 tocontrol the latter. It also supplies the synchronous addition timingsignal to the digital averager 21 to control the latter.

The laser driver 13 produces a very narrow driving pulse according tothe light-emission timing signal from the timing controller 12, andsupplies the driving pulse to the laser light source 14 to cause thelatter to emit pulsed-light.

The laser light source 14 produces pulsed-light of a predeterminedwavelength as long as the laser driver 13 is outputting the drivingpulse, and supplies the light pulse to the coupler 15.

The coupler 15 directs the pulsed-light from the laser light source 14to the incident end of the optical fiber 1 or the backscattered lightemitted from the incident end to the optical filter 16. It takes in thepulsed-light from the laser light source 14 and directs this to theincident end of the optical fiber 1. It then takes in the backscatteredlight which occurred as the pulsed-light was traveling in the opticalfiber 1 and which is emitted from the incident end, and directs it tothe optical filter 16.

The optical filter 16 takes in the backscattered light emitted from thecoupler 15 and separates the backscattered light into the anti-Stokescomponent and the Stokes component of the Raman spectrum throughwave-length discrimination. It then directs, to the optical selector 17,the anti-Stokes component and the Stokes component of the Raman spectrumof the backscattered light thus obtained.

The optical selector 17 selects one of the anti-Stokes component and theStokes component of the Raman spectrum of the backscattered lightsupplied from the optical filter 16 on the basis of the select signalfrom the CPU 22. It then directs to the photodiode 19 either theanti-Stokes component or the Stokes component of the Raman spectrum ofthe backscattered light thus obtained.

The bias controller 18 generates a bias voltage on the basis of the biasinstruction signal from the CPU 22, and supplies the bias voltage thusproduced to the photodiode 19.

The photodiode 19, biased with the bias voltage from the bias controller18, generates photocurrent according to the intensity of the anti-Stokescomponent or the Stokes component of the Raman spectrum of thebackscattered light emitted from the optical selector 17. It thensupplies the photocurrent generated to the photocurrent amplifier 20.

The photocurrent amplifier 20 produces a backscattered signal byamplifying the photocurrent from the photodiode 19. It then supplies thebackscattered signal thus obtained to the digital averager 21.

The digital averager 21 takes in the backscattered signal from thephotocurrent amplifier 20 on the basis of the synchronous additiontiming signal from the timing controller 12. It then performssynchronous addition of the backscattered signals to generate theaverage output of the anti-Stokes component or the Stokes component ofthe Raman spectrum of the backscattered light and supplies it to the CPU22.

The CPU 22 controls the entire temperature distribution sensingapparatus. The CPU 22 performs various processes, including the processof controlling the timing controller 12 and the bias controller 18 toadjust the light-emission timing and the synchronous addition timing,the process of taking in the average output of the anti-Stokes componentor the Stokes component of the Raman spectrum of the backscattered lightand storing it, the process of finding the optimum number of iterationsfor obtaining the inverse matrix used in deconvolution to obtain theimpulse response at the time of initialization or at predeterminedintervals during an actual measurement, the process of obtaining theimpulse response of the anti-Stokes component and the Stokes componentof the Raman spectrum of the backscattered light by performing theabove-described deconvolution on each stored average output in which theinverse matrix is obtained by an iteration method with the optimumnumber of iterations when the measurement instruction is issued andproducing a temperature signal from the ratio of these signals, and theprocess of out-putting the temperature signal obtained by the precedingprocess to the related circuit via the temperature distribution outputinterface.

The operation of determining the optimum number of iterations forobtaining the inverse matrix which is used in deconvolution to obtainthe impulse response and the temperature measuring operation in thefirst embodiment shown in FIG. 9 will now be described.

First, at the time of circuit initialization after the power of thetemperature distribution sensing apparatus is turned on, or each timethe predetermined correction timing is reached during an actualmeasurement, the CPU 22 of the signal processing device 3 takes in notonly the sensed data from the temperature sensor 5 to sense thetemperature in the room temperature enclosure 4 but also the sensed datafrom the temperature sensor 7 to verify whether or not the temperaturein the high-temperature enclosure 6 is at the predetermined temperature.

If the high-temperature enclosure 6 is not at the predetermined value,the CPU 22 controls the heater controller 9 to raise the temperature inthe high-temperature enclosure 6 to the predetermined temperature.

When the temperature in the high-temperature enclosure 6 has reached thepredetermined temperature, the CPU 22 controls the optical selector 17to select the anti-Stokes component of the Raman spectrum of thebackscattered light and then causes the timing controller 12 to drivethe laser driver 13. This causes the laser light source 14 connected tothe laser driver 13 to produce incident light pulse having a pulse widthvery narrow pulse width. The pulsed-light is supplied to the coupler 15.

The coupler 15 directs the pulsed-light to the optical fiber 1. Thebackscattered light undergoes wavelength discrimination with the opticalfilter 16, and is separated into the anti-Stokes component and theStokes component of the Raman spectrum of the backscattered light.

Because the optical selector 17 is switched to the anti-Stokes componentside, the anti-Stokes component obtained from the wavelengthdiscrimination process at the optical filter 16 is directed to thephotodiode 19 which converts it into photocurrent, and is amplified bythe photocurrent amplifier 20 into the anti-Stokes component signal.After this, the digital averager 21 performs synchronous addition on theanti-Stokes component signals a predetermined number of times to producethe average output of the anti-Stokes component signals. The averageoutput is supplied to the CPU 22, which stores it.

After this process is completed, the CPU 22 causes the optical selector17 to select the Stokes component of the Raman spectrum of thebackscattered signal and then causes the timing controller 12 to drivethe laser driver 13. This causes the laser light source 14 connected tothe laser driver 13 to produce incident light pulse having a very narrowpulse width. This pulsed-light is supplied to the coupler 15.

The coupler 15 directs the pulsed-light to the optical fiber 1. Thebackscattered light undergoes wavelength discrimination with the opticalfilter 16 and is separated into the anti-Stokes component and the Stokescomponent of the Raman spectrum of the backscattered light.

The optical selector 17 selects the Stokes component of the Ramanspectrum of the backscattered light obtained from the wavelengthdiscrimination process at the optical filter 16. The selectedbackscattered light is directed to the photodiode 19 which converts itinto photocurrent, and is amplified by the photocurrent amplifier 20into the Stokes component signal. After this, the digital averager 21performs synchronous addition on the Stokes component signals thepredetermined number of times to produce the average output of theStokes component signals. The average output is supplied to the CPU 22,which stores it.

After the averaging process of the anti-Stokes component signal and theStokes component signal is finished, the CPU 22 performs deconvolutionon the stored average outputs of the anti-Stokes component and theStokes component to obtain the respective impulse responses. It thengenerates a temperature signal from the ratio between these responses,and computes the total error of the temperature of the portions housedin the reference temperature chamber 2.

In this case, because the high-temperature portion placed in thehigh-temperature enclosure 4 of the reference temperature chamber 2 isshorter than the half-width of light pulse, it has not reached aparticular temperature expected from the heating temperature at first.By repeating deconvolution (multiplication of the inverse matrixobtained by an iteration method, i.e., by repeating the calculation ofthe inverse matrix), the high-temperature portion approaches the propervalue gradually. In this process, the random error is evaluated on thebasis of the temperature data on a sufficiently longer portion of theoptical fiber 1 than half the width of the light-pulse housed in theroom temperature enclosure 6 of the reference temperature chamber 2.

The number of iterations for calculating the inverse matrix that thetotal error is not less than that in the preceding calculation isdetermined to be the optimum number of iterations by the CPU 22, whichthen stores the optimum number.

After the operation of determining the above optimum number ofiterations is completed, the CPU 22 causes the optical selector 17 toselect the anti-Stokes component of the Raman spectrum of thebackscattered light and then causes the timing controller 12 to drivethe laser driver 13. This causes the laser light source 14 connected tothe laser driver 13 to produce incident light pulse having a very narrowpulse width. This light pulse is supplied to the coupler 15.

The coupler 15 then directs the pulse-light to the optical fiber 1. Thebackscattered light undergoes wavelength discrimination with the opticalfilter 16 and is separated into the anti-Stokes component and the Stokescomponent of the Raman spectrum of the backscattered light.

The optical selector 17 selects the anti-Stokes component obtained fromthe wavelength discrimination process at the optical filter 16. Theselected light is directed to the photodiode 19 which converts it intophotocurrent, and is amplified by the photocurrent amplifier 20 into theanti-Stokes component signal. After this, the digital averager 21performs synchronous addition on the anti-Stokes component signals thepredetermined number of times to produce the average output of theanti-Stokes component signals. The average output is supplied to the CPU22, which stores it.

After this process is complete, the CPU 22 causes the optical selector17 to select the Stokes component of the Raman spectrum of thebackscattered signal and then causes the timing controller 12 to drivethe laser driver 13. This causes the laser light source 14 connected tothe laser driver 13 to produce incident light pulse having a very narrowpulse width. This light pulse is supplied to the coupler 15.

The coupler 15 then directs the pulsed-light to the optical fiber 1. Thebackscattered light undergoes wavelength discrimination with the opticalfilter 16 and is separated into the anti-Stokes component and the Stokescomponent of the Raman spectrum of the backscattered light.

Then, the optical selector 17 selects the Stokes component of the Ramanspectrum of the backscattered light obtained from the wavelengthdiscrimination process at the optical filter 16 is directed to thephotodiode 19, which converts it into photocurrent. The photocurrent isamplified by the photocurrent amplifier 20 into the Stokes componentsignal. After this, the digital averager 21 performs synchronousaddition on the Stokes component signals the predetermined number oftimes to produce the average output of the Stokes component signals. Theaverage output is supplied to the CPU 22, which stores it.

After this process is complete, the CPU 22 performs deconvolution on thestored average outputs of the anti-Stokes component signal and theStokes component signal to obtain the respective impulse responses.Deconvolution is performed by multiplication of the inverse matrix ofthe incident light. The inverse matrix is calculated by an iterationmethod with the optimum number of iterations. Therefore, the impulseresponses thus obtained have a minimum error. Finally, the CPU 22obtains a temperature signal from the ratio between these impulseresponses and outputs the signal to the related circuit via thetemperature distribution output interface.

As described above, in the first embodiment, at the time ofinitialization and at regular intervals during an actual measurement, aportion of the optical fiber 1 is heated to a high temperature by thereference temperature chamber 2 with another portion kept at roomtemperature. In this state, the signal processing device 3 produces verynarrow pulsed-light and projects it into the optical fiber 1.Thereafter, it takes in the backscattered light (an averaged value),performs deconvolution on the anti-Stokes component and the Stokescomponent of the Raman spectrum of the backscattered light using theinverse matrix of the incident light calculated by an iteration methodto find the optimum number of iterations. To perform temperaturemeasurement, the signal processing device 3 generates very narrow lightpulse and projects it into the optical fiber 1. It then takes in itsbackscattered light, performs deconvolution on the anti-Stokes componentand the Stokes component of the Raman spectrum of the backscatteredlight using the inverse matrix calculated by an iteration method withthe optimum number of iterations to obtain the impulse responses of theanti-Stokes component and the Stokes component of the Raman spectrum ofthe backscattered light. This prevents the solution (the impulseresponse) from diverging under the influence of noise in deconvolution.As a result, it is possible to achieve the optimum approximation thatimproves the total accuracy most without narrowing the width of thelight pulse. In addition, the positional resolution can be improvedwithout a decrease in the signal-to-noise ratio due to a narrower widthof the pulsed-light, a consequent increase in the measuring time, or anincrease in the complexity of the semiconductor laser driver. Thisimprovement facilitates the sensing of abnormally heated portions suchas hot spots.

In the first embodiment, to obtain the optimum number of iterations, atleast a portion of the optical fiber shorter than half the width of theincident light pulse is heated or cooled and the heated or cooledportion is defined as a reference temperature portion. The number ofiterations that the total accuracy of the reference temperature portionis most improved is determined. A second embodiment related to anothermethod of finding the optimum number of iterations will be described.

In the second embodiment, instead of checking errors to find the optimumnumber of iterations that the error becomes the smallest, Fresnelreflected light from the incident end or terminal end of the opticalfiber is taken in as shown in FIG. 10, and deconvolution is performedusing the inverse matrix calculated by an iteration method. The optimumnumber of iterations is so determined that the waveform of the Fresnelreflected light after deconvolution becomes a streak like an impulseresponse. The actual measuring operation in the second embodiment is thesame as that in the first embodiment.

FIG. 11 shows the construction of the second embodiment. The same partsas those in the first embodiment are indicated by the same referencenumerals and their detailed explanation will be omitted.

The second embodiment is obtained by eliminating the referencetemperature chamber 2 from the first embodiment. The arrangement of thesignal processing device 3 is the same as that of the first embodiment.Specifically, in the second embodiment, which comprises the opticalfiber 1 and the signal processing device 3, at the time ofinitialization and at regular intervals during an actual measurement,the signal processing device 3 generates very narrow pulsed-light andprojects it into the optical fiber 1. It then takes in the Fresnelreflected light, performs deconvolution on the Fresnel reflected lightusing the inverse matrix calculated by an iteration method to determinethe optimum number of iterations. For an actual measurement, the signalprocessing device 3 generates very narrow pulsed-light and projects itinto the optical fiber 1. It then takes in its backscattered light,performs deconvolution on the anti-Stokes component and the Stokescomponent of the Raman spectrum of the backscattered light using theinverse matrix calculated by an iteration method with the optimum numberof iterations to measure the temperature distribution at each pointwhere the optical fiber 1 is laid.

The optical fiber 1 is laid so as to pass through each portion where thetemperature is to be measured. It, when pulsed-light has arrived at itsincident end, takes the pulsed light in and returns the backscatteredlight according to each portion and the Fresnel reflected light at theterminal end (the end on the opposite side of the incident end) to theincident end.

The signal processing device 3 comprises a timing controller 12, a laserdriver 13, a laser light source 14, a coupler 15, an optical filter 16,an optical selector 17, a bias controller 18, a photodiode 19, anoptical current amplifier 20, a digital averager 21, and a CPU 22. It,at the time of initialization and at regular intervals, generates verynarrow pulsed-light and projects it into the optical fiber 1, takes inthe Fresnel reflected light from the terminal end of the optical fiber 1and performs deconvolution on the Fresnel reflected light using theinverse matrix calculated by an iteration method to obtain the optimumnumber of iterations that the waveform of the signal corresponding tothe Fresnel reflected light takes the form of an impulse response.Because the Fresnel reflected light from the terminal end returns laterthan the backscattered light and its amplitude is much greater than thatof the backscattered light, it can be distinguished from thebackscattered light. For an actual measurement, as with the firstembodiment, the signal processing device 3 generates incidentpulsed-light having a very narrow pulse width and projects it into theoptical fiber 1. It then takes in its backscattered light, performsdeconvolution on the anti-Stokes component and the Stokes component ofthe Raman spectrum of the backscattered light using the inverse matrixcalculated by an iteration method with the optimum number of iterationsto measure the temperature distribution at each point where the opticalfiber 1 is laid.

The photodiode 19, which is an avalanche diode made of, for example,silicon, converts the anti-Stokes component or the Stokes component ofthe Raman spectrum of the backscattered light from the optical selector17 into photocurrent at a high amplification factor when the biasvoltage from the bias controller 18 is high, and supplies thephotocurrent to the photocurrent amplifier 20. When the bias voltagefrom the bias controller 18 is low, it converts the anti-Stokescomponent or the Stokes component of the Raman spectrum of thebackscattered light from the optical selector 17 into photocurrent at alow amplification factor (for example, an amplification factor of 1),and supplies the photocurrent to the photocurrent amplifier 20. Thereason for this is to cope with the difference in amplitude between theRaman spectrum of the backscattered light and the Fresnel reflectedlight.

The operation of the second embodiment will be explained. When thecircuitry is initialized after the power of this apparatus is turned onor each time a predetermined correction timing is reached, the CPU 22 ofthe signal processing device 3 causes the bias controller 18 to producea low voltage to make the amplification factor of the photodiode 19 low(for example, an amplification factor of 1). After this, the CPU 22causes the timing controller 12 to drive the laser driver 13. Thiscauses the laser light source 14 connected to the laser driver 13 togenerate incident light pulses having a very narrow pulsed-light. Thispulse width is supplied to the coupler 15.

The coupler 15 directs the pulsed-light to the optical fiber 1. TheFresnel reflected light is emitted from the terminal end of the opticalfiber 1, and the reflected light is directed via the optical filter 16and the optical selector 17 to the photodiode 19, which converts it intophotocurrent. After the photocurrent amplifier 20 amplifies thephotocurrent into a Fresnel reflected light signal, the digital averager21 performs synchronous addition a predetermined number of times toproduce the average output of Fresnel reflected light signals. Theaverage output is supplied to the CPU 22.

After this process is finished, the CPU 22 performs deconvolution on thestored average output of the Fresnel reflected light signal using theinverse matrix calculated by an iteration method and determines a numberof iterations such that the waveform of the Fresnel reflected lightcoincides with the desired linear waveform such as an impulse responsepreviously stored, to be the optimum number of iterations. It thenstores the optimum number.

After the operation of determining the optimum number of iterations iscompleted, the CPU 22 causes the optical selector 17 to select theanti-Stokes component signal and then causes the timing controller 12 todrive the laser driver 13. This causes the laser light source 14connected to the laser driver 13 to produce incident light pulse havinga very narrow pulse width. This pulsed-light is supplied to the coupler15.

The coupler 15 then directs the pulsed-light to the optical fiber 1. Thebackscattered light undergoes wavelength discrimination at the opticalfilter 16 and is separated into the anti-Stokes component and the Stokescomponent of the Raman spectrum of the backscattered light.

The optical selector 17 selects the anti-Stokes component obtained fromthe wavelength discrimination process at the optical filter 16. Theselected light is directed to the photodiode 19, which converts it intophotocurrent. The photocurrent is amplified by the photocurrentamplifier 20 into the anti-Stokes component signal. After this, thedigital averager 21 performs synchronous addition on the anti-Stokescomponent signals the predetermined number of times to produce theaverage output of the anti-Stokes component signals. The average outputis supplied to the CPU 22, which stores it.

After this process is complete, the CPU 22 causes the optical selector17 to select the Stokes component signal and then causes the timingcontroller 12 to drive the laser driver 13. This causes the laser lightsource 14 connected to the laser driver 13 to produce incident lightpulses having a very narrow pulsed-light. This pulse width is suppliedto the coupler 15.

The coupler 15 then directs the pulsed-light to the optical fiber 1. Thebackscattered light undergoes wavelength discrimination at the opticalfilter 16 and is separated into the anti-Stokes component and the Stokescomponent of the Raman spectrum of the backscattered light.

The optical selector 17 selects the Stokes component of the Ramanspectrum of the backscattered light obtained from the wavelengthdiscrimination process at the optical filter 16. The selected light isdirected to the photodiode 19 which converts it into photocurrent. Thephotocurrent is amplified by the photocurrent amplifier 20 into theStokes component signal. After this, the digital averager 21 performssynchronous addition on the Stokes component signals the predeterminednumber of times to produce the average output of the Stokes componentsignals. The average output is supplied to the CPU 22 and stored.

After this process is complete, the CPU 22 performs deconvolution on thestored average output of the anti-Stokes component signal and that ofStokes component signal by using the inverse matrix calculated by aniteration method with the optimum number of iterations, to obtain therespective impulse responses. Finally, it obtains the temperature signalfrom the ratio between these impulse responses and outputs the signal tothe related circuit via the temperature distribution output interface.

As described above, with the second embodiment, at the time ofinitialization and at regular intervals during an actual measurement,the signal processing device 3 generates incident light pulses having avery narrow pulse width and projects it into the optical fiber 1, takesin the Fresnel reflected light from the terminal end of the opticalfiber 1, and performs deconvolution on this Fresnel reflected lightusing the inverse matrix calculated by an iteration method to obtain theoptimum number of iterations that the waveform of the signalcorresponding to the Fresnel reflected light after deconvolution takesthe form of an impulse response. For an actual measurement, the signalprocessing device 3 generates incident light pulses having a very narrowpulse width and projects it into the optical fiber 1. It then takes inits backscattered light, performs deconvolution on the anti-Stokescomponent and the Stokes component of the Raman spectrum of thebackscattered light using the inverse matrix calculated by an iterationmethod with the optimum number of iterations to measure the temperaturedistribution at each point where the optical fiber 1 is laid. Thisprevents the solution, i.e., the impulse response, from diverging underthe influence of noise in an iteration process. As a result, it ispossible to achieve the optimum approximation that improves the totalaccuracy most without narrowing the width of the pulsed-light. Inaddition, the positional resolution can be improved without a decreasein the signal-to-noise ratio due to a narrower pulsed-light width, aconsequent increase in the measuring time, or an increase in thecomplexity of the semiconductor laser driver. This improvementfacilitates the sensing of abnormally heated portions such as hot spots.

In the second embodiment, to cope with the difference in amplitudebetween the Fresnel reflected light and the Raman spectrum of thebackscattered light, the value of the bias voltage applied to thephotodiode 19 is switched so as to make the amplification factorsmaller. When the intensity of the Fresnel reflected light is madealmost equal to the intensity of the anti-Stokes component or the Stokescomponent of the Raman spectrum of the backscattered light by applyingan attenuation coating to the incident and terminal ends of the opticalfiber 1, the Fresnel reflected light can be converted into photocurrentwithout the change of the bias voltage to the photodiode 19 and thesaturation of the photodiode 19, thereby providing a similar effect tothat of the above-described embodiments. Further, though in the abovedescription, the intensity of the intensity of the Fresnel reflectedlight is decreased by controlling the bias voltage applied to thephotodiode 19, it is not necessary to control the bias voltage appliedto the photodiode 19 if the Fresnel reflected light is sensed by theoptical filter 16 as shown in FIG. 11. It is to be noted that it ispossible to use either one of the Stokes component and the anti-Stokescomponent of the Fresnel reflected light. The light leaked out from theoptical filter 16 is decreased with reference to the incident light tothe filter 16. The filter 16 works as an attenuation means in the secondembodiment. On the contrary, if the bias voltage applied to thephotodiode 19 is controlled as described above, it is not necessary toprovide the optical filter 16.

As described above, according to the temperature distribution measuringapparatus of the present invention which improves the positionalresolution in the temperature distribution by obtaining the impulseresponse by performing deconvolution on the backscattered light usingthe inverse matrix of the incident light which is calculated by aniteration method, it is possible to prevent the solution of an iterationmethod, i.e., the inverse matrix, from diverging under the influence ofnoise. As a result, it is possible to achieve the optimum approximationthat improves the total accuracy most without narrowing the width of thelight pulse. In addition, the positional resolution can be improvedwithout a decrease in the signal-to-noise ratio due to a narrower lightpulse width, a consequent increase in the measuring time, or an increasein the complexity of the semiconductor laser driver. This improvementfacilitates the sensing of abnormally heated portions such as hot spots.

Additional advantages and modifications will readily occur to thoseskilled in the art. Therefore, the present invention in its broaderaspects is not limited to the specific details, representative devices,and illustrated examples shown and described herein. Accordingly,various modifications may be made without departing from the spirit orscope of the general inventive concept as defined by the appended claimsand their equivalents. For example, a successive over-relaxation method,a symmetric successive over-relaxation method, or the Chebyshevsemi-iterative method may be used as an iteration method for obtainingan inverse matrix of the incident light.

What is claimed is:
 1. An apparatus for measuring a temperaturedistribution along an optical fiber comprising:light source means forprojecting a light pulse into the optical fiber; optical filter meansfor receiving a Raman spectrum of backscattered light from the opticalfiber and extracting an anti-Stokes component and a Stokes component ofthe Raman spectrum in the backscattered light; means for performing adeconvolution a number of times on the Stokes component and theanti-Stokes component using an inverse matrix of the projected lightpulse to obtain an impulse response of the anti-Stokes component and animpulse response of the Stokes component, the inverse matrix beingobtained by an iteration method with an optimum number of iterations;means for obtaining a temperature distribution according to a ratiobetween the impulse responses of the anti-Stokes and the Stokescomponents; control means for causing said temperature distributionobtaining means to obtain a temperature distribution which includes anobtained temperature in a portion of the optical fiber as long as orshorter than a half of a pulse width of the light pulse, the portionhaving a known temperature, and for determining the obtained temperatureby performing a deconvolution a number of times such that an errorbetween the known temperature, and the obtained temperature is minimum;and wherein the number of times that the deconvolution is performed bythe performing means is equal to the number of times the deconvolutionis performed by the control means.
 2. An apparatus according to claim 1,wherein said impulse response is obtained using the following equation:##EQU4## where hi.sup.(k+1) is an i-th solution for a (k+1)th iteration,hi.sup.(k) is an i-th solution for a k-th iteration, d is a constant,and Pij is the inverse matrix of the light pulse projected into theoptical fiber.
 3. An apparatus according to claim 1, wherein the controlmeans determines the number of times the deconvolution is to beperformed when power to the apparatus is turned on or each time apredetermined period of time elapses in operation.
 4. A method ofmeasuring a temperature distribution along an optical fiber, comprisingthe steps of:heating a portion of the optical fiber to a predeterminedtemperature, the portion having a predetermined length; projecting afirst light pulse into the optical fiber, the first light pulse having apulse width, one half of which is longer than the predetermined lengthof said portion; receiving a first Raman spectrum in a firstbackscattered light from the optical fiber in response to said firstlight pulse and extracting a first anti-Stokes component and a firstStokes component of the first Raman spectrum in the first backscatteredlight; performing a deconvolution a number of times on the first Stokescomponent and the first anti-Stokes component using an inverse matrix ofthe projected first light pulse to obtain a first temperature signalbased on a result of the deconvolution, the number of times ofperforming the deconvolution being determined such that an error betweenthe first temperature signal and the predetermined temperature isminimized; projecting a second light pulse into the optical fiber, withsaid optical fiber placed in an area where a temperature distribution isto be measured; receiving a second Raman spectrum in a secondbackscattered light from the optical fiber in response to said secondlight pulse and extracting a second anti-Stokes component and a secondStokes component of the second Raman spectrum in the secondbackscattered light; and performing a deconvolution a number of times onthe second Stokes component and the second anti-Stokes component usingan inverse matrix of the projected second light pulse to obtain a secondtemperature signal based on a result of the deconvolution on the secondStokes and anti-Stokes components, the number of times of performing thedeconvolution on the second Stokes and anti-Stokes components beingequal to the number of times of performing the deconvolution on thefirst Stokes and anti-Stokes components, the second temperature signalcorresponding to the temperature distribution along the optical fiber.